Automorphism groups of Ree type Deligne-Lusztig curves and function fields.
Automorphy for some l-adic lifts of automorphic mod l Galois representations. II
We extend the results of [CHT] by removing the ‘minimal ramification’ condition on the lifts. That is we establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), l-adic lifts of certain automorphic mod l Galois representations of any dimension. The main innovation is a new approach to the automorphy of non-minimal lifts which is closer in spirit to the methods of [TW] than to those of [W], which relied on Ihara’s lemma.
Automorphy for some l-adic lifts of automorphic mod l Galois representations
We extend the methods of Wiles and of Taylor and Wiles from GL2 to higher rank unitary groups and establish the automorphy of suitable conjugate self-dual, regular (de Rham with distinct Hodge–Tate numbers), minimally ramified, l-adic lifts of certain automorphic mod l Galois representations of any dimension. We also make a conjecture about the structure of mod l automorphic forms on definite unitary groups, which would generalise a lemma of Ihara for GL2. Following Wiles’ method we show that this...
Auxiliary polynomials for some problems regarding Mahler's measure
Average Frobenius distributions for elliptic curves over abelian extensions
Average r-rank Artin conjecture
Let Γ ⊂ ℚ * be a finitely generated subgroup and let p be a prime such that the reduction group Γₚ is a well defined subgroup of the multiplicative group ₚ*. We prove an asymptotic formula for the average of the number of primes p ≤ x for which [ₚ*:Γₚ] = m. The average is taken over all finitely generated subgroups , with and , with a range of uniformity for every i = 1,...,r. We also prove an asymptotic formula for the mean square of the error terms in the asymptotic formula with a similar...
Average values of L-series in function fields.
Bases d'entiers dans les extensions cycliques de degré 4 de Q
Bases for cyclotomic units
Bases normales d'entiers dans les extensions de Kummer de degré premier
Si est un corps de nombres, on note son anneau d’entiers ; si est une extension galoisienne finie de corps de nombres de groupe de Galois , on appelle base normale de sur toute base de en tant que -module de la forme avec . On démontre dans ce travail un critère d’existence de base normale d’entiers pour les extensions de Kummer de degré premier, qui permet une construction explicite en cas d’existence ; les principaux outils pour la démonstration sont une formule de Fröhlich pour...
Bases normales d'entiers et unités modulaires.
Bases normales et constante de l’équation fonctionnelle des fonctions d’Artin
Bases normales relatives en caractéristique positive
Dans cet article, nous étudions la structure galoisienne des anneaux d’entiers des corps de fonctions cyclotomiques dans le cas modéré. Nous montrons qu’en général, si le corps de base est de genre plus grand que , ces anneaux ne sont pas libres sur les anneaux de groupes considérés.
Bases normales, unités et conjecture faible de Leopoldt.
Bases of canonical number systems in quartic algebraic number fields
Canonical number systems can be viewed as natural generalizations of radix representations of ordinary integers to algebraic integers. A slightly modified version of an algorithm of B. Kovács and A. Pethő is presented here for the determination of canonical number systems in orders of algebraic number fields. Using this algorithm canonical number systems of some quartic fields are computed.
Beitrag zur Theorie gewisser complexer Zahlen.
Bemerkung uber zwei Satze von Jakowkin
Bemerkungen zu einer metrischen Invarianten algebraischer Zahlkörper.
Bemerkungen zum Satz von Heegner-Stark über die imaginär-quadratischen Zahlkörper mit der Klassenzahl Eins.
?ber singul?re Invarianten elliptischer Funktionenk?rper.